I was reading Hugh Osborne's notes on Conformal Field theory and came across a completeness relation which seems easy to prove but I am unable to do it.


where the spin matrices $s_{\mu\nu}$ are defined by


It would be highly helpful if someone can just sketch the proof.

  • $\begingroup$ Which of the two equalities do you have trouble proving? Both of them? $\endgroup$ – M.Jo Jul 3 at 11:06
  • $\begingroup$ First equality is specific for d=3 I suppose and I proved it. But in the second equality I am getting a factor of 4 wrong. $\endgroup$ – spyk_speigel Jul 10 at 8:46

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